Abstract The present study numerically investigated the entropy production in nanofluids' dissipative unsteady oscillatory flow characterised by variable electric conductivity and magnetic heating effects. The imposition of the non-isothermal boundary condition on the oscillatory stretching sheet plays a crucial role in establishing the self-similar solution in the presence of viscous heating. An external magnetic field (uniform in space and time) is imposed perpendicular to the plane of the oscillating stretched boundary. The energy equation, incorporating viscous dissipation effects and momentum equation, is reduced to nonlinear coupled partial differential equations and numerically solved using the Gear-generalized differential quadrature scheme. The Corcione model is implemented to describe the nanofluid's effective viscosity and thermal conductivity. Furthermore, expressions for entropy production and relative irreversibility parameter (Bejan number), considering variable electric conductivity, are derived and computed based on solutions obtained from momentum and energy equations. The impacts of parameters such as magnetic parameter, variable electric conductivity parameter, Eckert number, Strouhal number, Prandtl number and temperature difference parameters on flow, heat transfer, entropy generation, and Bejan number are systematically illustrated and examined. We observed that increasing the variable electric conductivity parameters reduces the velocity profiles while improving the thermal fields. Similar behaviour is found when the strength of a magnetic field is increased. The skin friction coefficient exhibits an augmentation in response to the Eckert number, dimensionless time, Strouhal number, nanoparticle volume fraction, magnetic parameter, and variable thermal conductivity parameter. Conversely, the Nusselt number increases concerning the Strouhal number and nanoparticle volume fraction. At the same time, it declines in association with the magnetic parameter, dimensionless time, Eckert number, and variable electric conductivity parameter. Additionally, to ensure the precision and reliability of the outcomes, the numerical code undergoes a thorough validation process that involves comparing its outputs to the findings of previous available studies. This comprehensive investigation enhances our understanding of nanofluid dynamics and provides valuable insights for optimising thermal management systems across various engineering disciplines.